Lecture Notes 3

EPF 0024: Physics II 1

3.0 Electric Current


Outline

3.1 Production of direct electric current3.2 Ohm’s Law3.3 Resistivity3.4 Electric Energy and Power


Today's lecture Include:

Production of direct electric current

Ohm’s Law


Objectives

To explain the basic principles of a simple cell and define the electric current.

State and explain Ohm’s law.

Solve Problems.


3.1 Principle of a Simple Cell

A simple cell (Fig. 3.1) consists of:

1. Two rods (electrodes) made of dissimilar metals such as carbon and zinc

2. A solution, e.g. diluted sulfuric acid (electrolyte).

The terminals of the cell is the portion of the electrode outside the electrolyte. A Battery are several cells connected together (in series).


Fig. 3.1 A Simple Electric Cell

Acid

+ Zinc electrode ()Carbon electrode (+)

+ Terminal Terminal

Electrical symbol for a cell


3.1.1 Operation of a simple cell

Electrolyte dissolves zinc and each zinc atom leaves 2 electrons behind and enters the electrolyte as positive ion making zinc electrode –vely charged and electrolyte +vely charged. The +ve electrolyte pulls off electrons from the carbon electrode making it +vely charged and a p.d. now exists between the two terminals.

The p.d. (voltage) that exists between terminals is called the electromotive force (emf). Allowing charges to flow externally results in more zinc being dissolved to maintain constant voltage at terminals. Eventually, the zinc will be used.


3.1.2 The Electric Current

An electric circuit is formed when a conductor is connected between the terminals of a cell (Fig. 3.2 (a)). Closing the switch S results in a net motion of electrons from the negative terminal to the positive terminal.

This motion of charges is represented by the flow of what is known as the conventional electric current from the positive terminal to the negative as shown in Fig. 3.2 (b).


Fig. 3.2 (a) The flashlight (simple electric circuit) and (b) direction of current & electron flow.

(a) (b)

S


The electric current I is defined as the net amount of charge that passes through a given cross-section of a conductor per unit time:

(3.1)

The SI unit of I is coulomb per second (C/s) and is known as the ampere (symbol: A).

tQI

tQI

Constant current

Variable current


Example

A steady current of 2.5 A flows in a wire for 4.0 minutes. (a) How much charge pass through any point in the circuit. (b) How many electrons would this be.


Solution

(a)

(b)

C 600s 604C/s 5.2 Itq

electrons. 108.3

C101.6C 600 21

19

eqn

neq


3.5 Ohm’s Law

States: The current flowing through a conductor is directly proportional to the potential difference applied to its ends.

Where the proportionality constant R is called resistance (units = ohm ()).

IR VRVI or (3.2)

Circuit symbol for R


Fig. 3.3: I versus V for conductors

RVI 1slope

I (A)

V (V)

I

V

I as a function of V is a straight line through the origin (Fig. 3.3).


Resistors are an indispensable part of all electronic components (Fig. 3.4).

Fig. 3.4 Electronic components


Table 3.1: Color code for resistorsColor 1st digit 2nd digit Multiplier Tolerance (%)

Black 0 0 1

Brown 1 1 10

Red 2 2 102

Orange 3 3 103

Yellow 4 4 104

Green 5 5 105

Blue 6 6 106

Violet 7 7 107

Grey 8 8 108

White 9 9 109

Gold 0.1 5

Silver 0.01 10

No color 20

Table 3.1 shows the convention to determine the value of a resistor using color codes.


Fig. 3.5: Decoding of actual resistor value

1st digit (red)

2nd digit (green)

Tolerance (silver)

Multiplier (orange)

Using the color code in Table 3.1 the resistor value is determined to be 25 k ± 10%.

Fig. 3.5 is an example indicating the decoding of the actual value of a resistor.


Example 1

A small flashlight bulb draws 300 mA from its 1.5 V battery. (a) What is the resistance of the bulb? (b) If the voltage is dropped to 1.2 V, how would the current change?


Solution

(a) Applying Ohm’s law we find:

(b) If the voltage drops to 1.2 V, assuming the resistance stayed constant, then

Ω 0.5

A 0.3V 5.1

IVR

mA. 60 of drop aor A 24.0

Ω 5.0V 2.1

RVI


3.6 Resistivity

For conductors:

(3.3)

Where is resistivity, L length and A cross-sectional area. From equation (3.3) we deduce the SI unit of resistivity to be .m.

ALρR

ALR or


Example

Given that the resistivity of a copper wire is 1.7 108 .m. Find (a) the diameter of a 20-m circular wire if the resistance of the wire is 0.10 . (b) What is the voltage drop across the wire if the current flowing through the wire is 12 A.


Solution

(a)

mm 2.1m101.2

Ω 0.10m 20Ω.m107.14

4

4

38

2

RLd

dL

ALR

(b) Using Ohm’s

V 1.2

Ω 10.0A 12 IRV


Today's lecture Include:

Temperature Effect on Resistance.

Superconductivity.


Objectives

Explain the effect of increasing temperature on resistance.

Explain superconducting effect.

Consider some applications related to these concepts.


3.7 Temperature Effect on Resistance

Resistivity of metals increases linearly with increasing temperature (for moderate temperatures of up to 300oC) according to:

where o is the resistance at 0oC and is temperature coefficients of resistivity. The reason is that atoms vibrate more rapidly at higher temperatures and interfere with the flow of electrons through the material causing the it to have a higher resistance.

)1( ToT (3.4)


3.7.1 Resistance Thermometer

The variation of electrical resistance with temperature is used to make precise temperature measurement.

Suppose at 0C resistance R of a platinum is 164.2 . When placed in a solution, R increases to 187.4 . What is the temperature of the solution if temperature coefficient of resistivity is 3.927 103 (oC)1?


Since resistance R is directly proportional to resistivity (), we can write equation 3.5 as

where R0 = 0L/A is the resistance at 0oC.

C35.9

Ω 2.164C103.927Ω 2.164Ω 4.187C0 where1

o

1o30

0

0

RRRT

TTTTRR o


3.7.2 Superconductivity

At low temperatures the resistance of certain metals and their alloys drop to zero. The effect is termed superconductivity and materials exhibiting the phenomenon are called superconductors.

It was first observed by Onnes in 1911, when mercury was cooled down to below 4.2 K. In general materials become superconducting within a few degrees of absolute zero.


Resistivity of superconductors is practically zero. Current in a ring-shaped super conducting coil has been observed to flow for years in the absence of a potential difference.

Earlier, the highest temperature at which superconductivity is achieved was 23K and so requires liquid hydrogen cooling. Currently some alloys have been developed that can be superconducting at 90 K requiring cooling in boiling liquid nitrogen.


Advantages of superconductivity :

(i) Smaller electric motors and generators. Electric cars will be practical.

(ii) Less power lost on transmission lines and use of thinner wires feasible (cost saving).

(iii) Faster computer and more efficient high speed train levitation.

Lecture Notes 3

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